Numerous analytical instruments operate by directing particles and/or radiation (photons) at a specimen, and then measuring the number and energy of particles/photons emitted by the specimen in response. For example, in an X-ray fluorescence spectrometer, X-rays and/or gamma rays are directed at a specimen, and as the atoms of the specimen ionize in response to the incident radiation, photons are emitted with energies characteristic of the specimen's component atoms. The energies of the photons are then measured by a detector along with their time of detection. By compiling a spectrum containing the numbers and energies of the emitted photons and comparing it to reference spectra (spectra generated from known substances), one may obtain information regarding the substances present in the specimen.
However, difficulties often arise with the accurate measurement of photon energies. This is best understood with reference to FIGS. 1a-1d, which illustrate the output of a detector (e.g., a Silicon Drift Detector (SDD), Lithium-drifted Silicon (Si(Li)) detector, photodiode, silicon multi-cathode detector (SMCD), PiN diode, or other particle/photon sensor). The detector usually has a step-like output as exemplified in FIG. 1a, wherein each point along the signal trace represents a sampled measurement from the detector. Each step (rise) along the signal trace occurs at the time of particle/photon detection, with the height of the step being correlated to the energy of the particle/photon. Such detector output may be translated into different forms for analysis; for example, in FIG. 1b, the signal of FIG. 1a is differentiated by passing it through a high-pass filter, and in FIG. 1c, the signal of FIG. 1b is converted to a spike-like form by subtracting from each point the value of the prior point, and applying a decaying exponential to account for the slope arising from the filter's differentiation. The time and energy of each spike in FIG. 1c then represents the time and energy of each detected particle/photon. Regardless of the form of the detector output signal used for analysis, the objective is to obtain an accurate determination of the energy at each rise or spike—generally referred to as an “event” (with “event” referring to the receipt of a particle/photon)—so that a spectrum can be generated, i.e., a distribution of the energies of the events (the detected particles/photons). The spectrum is often displayed to the user in the form of a histogram showing intervals of event energies and the number (count) of events falling within each interval, with an exemplary spectrum being shown in FIG. 2.
A spectrum has greater value if the energies of its events are measured with higher resolution, since this eases comparison of the measured spectrum with reference spectra. One could measure event energies by simply subtracting the energy of the point before each event (rise) in FIGS. 1a and 1b from the energy of the point after each event, or by measuring the maximum energy of each event (spike peak) in FIG. 1c. However, owing to the background noise of the detector—best seen by the variations about zero energy in FIG. 1c at the times where no spikes exist—this does not result in highest resolution. It is therefore conventional to determine event energies from signals such as those in FIG. 1a by applying the concept of a “shaping time”: the average of the energies of several points prior to the event—all points fitting within some defined time interval prior to the event—are subtracted from the average of the energies of several points after the event (here all points fitting within the same time interval applied after the event). For example, in FIG. 1a, looking to the first event (occurring around 5850 microseconds) and applying a 30 microsecond shaping time, the average of the energies over a 30 microsecond shaping time prior to the rise (as indicated by the first point having significantly higher value) may be subtracted from the average of the energies in the 30 microseconds thereafter to obtain a measure of the event energy. The result is a measurement of the event energy with significantly higher resolution. (Note that points are often sampled during the rise itself, and to avoid their skewing of the averaged pre-event and/or post-event energies, these are often excluded from the averaging. This is often done by determining the start of an event by use of some discrimination algorithm which locates points which have a significant value change with respect to the energy of a prior point, with the prior point then being the last pre-event point, and then locating the points thereafter which do not exhibit significant value changes, with the first of these representing the first pre-event point.)
The shaping time concept can also be applied to signals such as those in FIG. 1c by taking, at each point, the sum of some number of prior points falling within a defined time interval before the point in question. This results in a signal such as that shown in FIG. 1d, wherein each event in FIG. 1c is now represented by a pulse (and with summing at each point here occurring over the last 30 microseconds). In this case, the shaping time is usually referred to as a “moving window,” since points are summed over a moving window of time analogous to the shaping time. Here, again looking to the first event (at about 5850 microseconds), one can then average the energies over the pulse to obtain a higher resolution measurement of the energy of the event.
However, the foregoing methods of determining event energies become problematic when events are closely spaced in time, more specifically when they are spaced by less than the shaping time. This can be understood with reference to the third and fourth events shown in FIGS. 1a-1d, i.e., the events occurring at around 6065 and 6085 microseconds. If one considers use of the aforementioned exemplary 30 microsecond shaping time to the third (6065 microsecond) event of FIG. 1a, it is clear that an accurate measure of the pre-event energy can be obtained: the pre-event energies are relatively constant over the 30 microseconds prior to the event, and thus averaging these values will provide a good representative value of the pre-event energy. However, since another event occurs within the 30 microseconds thereafter, an average of the post-event points over these 30 microseconds will be inaccurate—it will not accurately reflect the value of the post-event energy occurring after 6065 microseconds and prior to the 6085 microsecond event. The determination of the energy of the fourth event at 6085 microseconds will also be inaccurate with a 30 microsecond shaping time because the pre-event energy will not be accurately reflected by an average of the points over the 30 microseconds prior to the event. As a result, the third and fourth events would not be counted when collecting the event energies and generating the spectrum. The period spanning the shaping time prior to and after an event is often referred to as “dead time”: no other events can be detected during the dead time, or else all events therein must be discarded because their energies cannot be determined with the desired resolution. In essence, dead time reflects time which cannot be used to collect events, and it is therefore desirable to reduce dead time to increase throughput (event collection rates).
The problem of discarded dead time events is not avoided when analyzing the detector signal in other forms, such as the forms of FIGS. 1b-1d. For example, when the signal of FIG. 1d is analyzed, averaging the energies at the top of the first and second pulses over a 30 microsecond moving window will provide a useful measurement of the event energies of the first and second events, but averaging the energies over the 30 microseconds following the third (6065 microsecond) and fourth (6085 microsecond) events will not yield an accurate measure of these events.
The foregoing problem—the condition where two or more events occur during the shaping time, requiring that they be excluded from the spectrum is often referred to as “pile-up,” and it is significant because it occurs very often. It is not uncommon for as many as 50% of the events captured during spectral measurements to be discarded owing to pile-up. This is disadvantageous because the ability to accurately compare a spectrum to reference spectra increases with the spectrum's event count. There are ways to reduce or avoid discarded dead time events, such as by reducing the shaping time; for example, averaging pre- and post-event energies before and after the third and fourth events of FIG. 1a over a 5 microsecond shaping time would seem to avoid the problem of including an extra event within an average. However, since pre- and post-event energies are determined with better resolution with longer shaping times, a shorter shaping time results in a lower-resolution measure of event energies. It is also possible to use a variable shaping time—for example, by determining the pre-event energy for the third event over a 30 microsecond shaping time, and then applying a post-event shaping time of 5 microseconds to avoid inclusion of the forth event. This methodology also has disadvantages because it results in a spectrum wherein the event energies have varying resolutions. Another solution is to increase event counts by increasing the time over which the specimen is analyzed, but increasing analysis time increases inconvenience, since analysis results are usually desired as soon as feasibly possible.